STATE-FEEDBACK AND ESTIMATION OF WELL-POSED SYSTEMS

The class of well-posed systems includes many systems modeled by partial differential equations with boundary control and point sensing as well as many other systems with possibly unbounded control and observation. The closed-loop system created by applying state-feedback to any well-posed system is well-posed. A state-space realization of the closed loop is derived. A similar result holds for state estimation of a well-posed system. Also, the classical state-feedback/estimator structure extends to well-posed systems. In the final section state-space realizations for a doubly coprime factorization for well-posed systems are derived.